RNA polymerase III (pol III) transcription generally terminates at a run of four or more thymidine (T) residues but some pol III genes contain runs of T residues that are not recognized as termination signals. Here, we investigate the terminal signal requirements that are operative in adenovirus virus-associated (VA) RNA genes. In the Xenopus 5 S RNA gene, efficient termination requires the T residues to be in a G+C-rich sequence context, but a run of five T residues in a G+C-rich context does not cause pol III termination when placed 30 nt downstream of the adenovirus-2 VA RNAI promoter in a VA-Tat chimeric gene. The failure of pol III to recognize this putative termination signal is not due to the chimeric nature of the gene or to the proximity of the signal to the promoter, but to its sequence context. Termination at the VA RNA gene site requires a T-rich sequence and is inhibited by the proximity of G residues, but is insensitive to the presence of A residues. The T-rich sequence need not be uninterrupted, however. In the VA RNA gene of the avian adenovirus, CELO, the first of two tandem termination signals contains an interrupted run of T residues, TTATT, which functions as a terminator with high (although not complete) efficiency. These findings, together with a survey of sequences neighboring the terminal site of other pol III genes, lead to the conclusion that pol III termination signals are more complex than hitherto recognized, and that sequence context requirements differ between members of the class 1 and class 2 families of pol III genes.